Lorenz system
Generates a 3-dimensional time series using the Lorenz equations.
lorenz( sigma = 10, beta = 8/3, rho = 28, start = c(-13, -14, 47), time = seq(0, 50, by = 0.01), do.plot = TRUE )
sigma |
The sigma parameter. Default: 10. |
beta |
The beta parameter. Default: 8/3. |
rho |
The rho parameter. Default: 28. |
start |
A 3-dimensional numeric vector indicating the starting point for the time series. Default: c(-13, -14, 47). |
time |
The temporal interval at which the system will be generated. Default: time=seq(0,50,by = 0.01). |
do.plot |
Logical value. If TRUE (default value), a plot of the generated Lorenz system is shown. |
The Lorenz system is a system of ordinary differential equations defined as:
dx/dt = sigma*( y - x )
dy/dt = rho*x - y - xz
dz/dt = -beta*z + xy
The default selection for the system parameters (sigma=10, rho=28, beta=8/3) is known to produce a deterministic chaotic time series.
A list with four vectors named time, x, y and z containing the time, the x-components, the y-components and the z-components of the Lorenz system, respectively.
Some initial values may lead to an unstable system that will tend to infinity.
Constantino A. Garcia
Strogatz, S.: Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering (Studies in Nonlinearity)
## Not run: lor=lorenz(time=seq(0,30,by = 0.01)) # plotting the x-component plot(lor$time,lor$x,type="l") ## End(Not run)
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